### Video Transcript

Determine the length of line
segment π΄π·.

We note that π· is the projection
of π΄ onto the line π΅πΆ and that the triangle π΄π΅πΆ is a right triangle at π΄. And we recall that the corollary to
the Euclidean theorem, that is, the altitude rule, tells us that π΄π· squared is
equal to π΅π· multiplied by πΆπ·. This tells us that the altitude or
height of the right triangle squared is the product of the lengths of the segments
of the hypotenuse when it is split by the altitude.

Weβre given that the two segments
are 2.5 centimeters, thatβs πΆπ·, and 6.4 centimeters, thatβs π΅π·. And substituting these values in,
we have π΄π· squared is 6.4 multiplied by 2.5. This evaluates to 16, so π΄π·
squared is 16. Now, taking the square root on both
sides of the equation, noting that π΄π· is a length and so is nonnegative, we get
π΄π· is the square root of 16, which is four. The length of π΄π· is therefore
four centimeters.